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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-rngc | Structured version Visualization version Unicode version |
Description: Definition of the category Rng, relativized to a subset . This is the category of all non-unital rings in and homomorphisms between these rings. Generally, we will take to be a weak universe or Grothendieck universe, because these sets have closure properties as good as the real thing. (Contributed by AV, 27-Feb-2020.) (Revised by AV, 8-Mar-2020.) |
Ref | Expression |
---|---|
df-rngc | RngCat ExtStrCat cat RngHomo Rng Rng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crngc 41957 | . 2 RngCat | |
2 | vu | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | 2 | cv 1482 | . . . . 5 |
5 | cestrc 16762 | . . . . 5 ExtStrCat | |
6 | 4, 5 | cfv 5888 | . . . 4 ExtStrCat |
7 | crngh 41885 | . . . . 5 RngHomo | |
8 | crng 41874 | . . . . . . 7 Rng | |
9 | 4, 8 | cin 3573 | . . . . . 6 Rng |
10 | 9, 9 | cxp 5112 | . . . . 5 Rng Rng |
11 | 7, 10 | cres 5116 | . . . 4 RngHomo Rng Rng |
12 | cresc 16468 | . . . 4 cat | |
13 | 6, 11, 12 | co 6650 | . . 3 ExtStrCat cat RngHomo Rng Rng |
14 | 2, 3, 13 | cmpt 4729 | . 2 ExtStrCat cat RngHomo Rng Rng |
15 | 1, 14 | wceq 1483 | 1 RngCat ExtStrCat cat RngHomo Rng Rng |
Colors of variables: wff setvar class |
This definition is referenced by: rngcval 41962 |
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